Mathematical Physics
Explore fields and transforms; variational and spectral methods; symmetry and conservation. Concepts and connections are available independently of video coverage.
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Distributions as generalized functions
A distribution acts linearly and continuously on test functions, allowing generalized derivatives.
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Fourier series
Periodic functions can be expanded in harmonic components with convergence interpreted under suitable hypotheses.
Green's functions
A Green's function is a kernel representing a linear operator's response to a point source with specified boundary conditions.
Calculus of variations
Variational calculus studies extrema of functionals depending on functions.
Dimensional similarity
Dimensionless groups compare physical systems while respecting the dimensions of quantities.
Euler–Lagrange equations
Stationarity of a smooth variational problem gives differential conditions with appropriate boundary constraints.
Knowledge connections
- Green's functions · Related · Map context
- Fourier series · Related · Map context